Title of article :
PBIB Designs and Association Scheme Arising from Minimum Total Dominating Sets of
Non Square Lattice Graph
Author/Authors :
Shekharappa، H.G. نويسنده Visveswaraya Technological University,Karnataka,India , , Shirkol، Shailaja S. نويسنده Department of Mathematics,SDM College of Engineering and Technology,Karnataka,India , , Gudgeri، Manjula C. نويسنده Department of Mathematics,KLE Dr. M. S. Sheshagiri College of
Engineering and Technology,Karnataka,India ,
Issue Information :
ماهنامه با شماره پیاپی سال 2013
Abstract :
Square lattice graphs L_2 (n) with the parameters (n^2, 2(n-1), n-2, 2)
are strongly regular and are unique for all n except n=4. however for n=4, we have two non-isomorphic strongly regular graphs. The non-lattice graph with parameters (16,6,2,2 ) is known
as Shrikhande graph. In this paper we show that every minimum total
dominating set in Shrikhande graph induces two K_2s. Further
we establish that these classes of minimum total dominating sets of
Shrikhade graph form Partially Balanced Incomplete Block Designs with
the parameters (16, 44, 11, 4, λi, i=1or2, λij=3or4).
Keywords :
Partially Balanced Incomplete Block Designs , Minimum total
dominating set , Total domination number , Strongly regular graph
Journal title :
General Mathematics Notes
Journal title :
General Mathematics Notes
